ARTICLE

Received 8 Jun 2014 | Accepted 5 Aug 2014 | Published 15 Sep 2014

Electrically tuned magnetic order andmagnetoresistance in a topological insulatorZuocheng Zhang1,*, Xiao Feng1,2,*, Minghua Guo1, Kang Li2, Jinsong Zhang1, Yunbo Ou2, Yang Feng1,

Lili Wang1,2,3, Xi Chen1,3, Ke He1,2,3, Xucun Ma1,2,3, Qikun Xue1,3 & Yayu Wang1,3

The interplay between topological protection and broken time reversal symmetry in

topological insulators may lead to highly unconventional magnetoresistance behaviour that

can find unique applications in magnetic sensing and data storage. However, the

magnetoresistance of topological insulators with spontaneously broken time reversal

symmetry is still poorly understood. In this work, we investigate the transport properties of a

ferromagnetic topological insulator thin film fabricated into a field effect transistor device. We

observe a complex evolution of gate-tuned magnetoresistance, which is positive when the

Fermi level lies close to the Dirac point but becomes negative at higher energies. This trend is

opposite to that expected from the Berry phase picture, but is intimately correlated with

the gate-tuned magnetic order. The underlying physics is the competition between the

topology-induced weak antilocalization and magnetism-induced negative magnetoresistance.

The simultaneous electrical control of magnetic order and magnetoresistance facilitates

future topological insulator based spintronic devices.

DOI: 10.1038/ncomms5915

1 Department of Physics, State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, P. R. China. 2 Institute of Physics,Chinese Academy of Sciences, Beijing 100190, P. R. China. 3 Collaborative Innovation Center of Quantum Matter, Beijing 100084, P. R. China. * These authorscontributed equally to this work. Correspondence and requests for materials should be addressed to K.H. (email: kehe@tsinghua.edu.cn) or to Y.W.(email: yayuwang@tsinghua.edu.cn).

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The studies of magnetoresistance (MR) in novel magneticmaterials have been at the center stage in the field ofspintronics1. The most notable example is the discovery of

giant MR when two ferromagnetic (FM) films separated by anonmagnetic spacer layer have anti-parallel alignment2. Giant MRnot only reveals the remarkable consequence of spin-dependenttransport, but also caused a revolution in information technology.The recently discovered topological insulators (TIs) possess Dirac-like surface states that are protected by time reversal symmetry(TRS) and exhibit a host of novel properties3–5. Introducingmagnetism into TI, which breaks the TRS, is expected to createexotic topological magnetoelectric effects6–10. In a naıve picture, aTI film with long-range FM order can be viewed as a bulkferromagnet sandwiched between two layers of Dirac fermionswith opposite chiralities, as illustrated in Fig. 1a. The MRbehaviour in such a system is apparently of tremendous interest,but experimental challenges associated with magnetically dopedTI have hindered a thorough exploration of this phenomenon.For example, recent studies show that Cr-doped Bi2Se3, which ispresumably the best TI, remains paramagnetic in spite of increasedCr content11. Transition metal-doped Sb2Te3 exhibit robustFM order12,13, but the charge transport is dominated by bulkcarriers rather than the topological surface states. The most idealsituation, of course, is to have a TI film with spontaneous FM orderand tunable Fermi level (EF) over a wide doping range across theDirac Point (DP).

In this work, we achieve these goals by growing magneticallydoped TI film with chemical formula Cr0.15(Bi0.1Sb0.9)1.85Te3 andfabricating it into a field effect transistor device, as schematicallydrawn in Fig. 1b. The mixing of Bi/Sb can tune the band structureclose to an ideal TI14, and when doped with Cr, the systemexhibits bulk FM order with out-of-plane easy axis15. Theelectrical gate can drive EF to various regimes of the TI bandstructure. Details about sample growth, device fabrication andmeasurements are presented in Methods and SupplementaryNote 1.

Our transport measurements on such a field effect transistordevice reveal an unusually complex evolution of MR when EF istuned across the DP by gate voltage. In particular, MR tends to bepositive when EF lies close to the DP but becomes negative athigher energies. This trend is opposite to that expected from theBerry phase picture for localization, but is intimately correlatedwith the gate-tuned magnetic order. We show that the underlyingphysics is the competition between the topology-induced weakantilocalization (WAL) and magnetism-induced negative MR.The simultaneous electrical control of magnetic order andmagnetotransport facilitates future TI-based spintronic devices.

ResultsDemonstration of FM order in the sample. Figure 1d displaysthe temperature (T) dependent two-dimensional (2D) Hallresistivity (ryx) measured at varied gate voltages (Vg). At thelowest T¼ 1.5 K, the square-shaped hysteretic Hall traces for allVg indicate robust FM order. The total ryx in this case can beexpressed as ryx¼RAMþRHH. Here, M is the magnetization ofthe sample and RA/RH is the anomalous/ordinary Hall coefficient,respectively. With increasing Vg from � 15V to þ 15V, the RHat T¼ 1.5 K changes from positive to negative, indicating thechange from p- to n-type charge carriers via the bulk insulatingregime. The existence of robust ferromagnetism across the entireVg range is similar to that observed in Cr-doped (Bi,Sb)2Te3 filmswith varied Bi/Sb ratio15. The FM order becomes weaker withincreasing T and disappears for all Vg at T¼ 15K, when the Hallcurves become reversible but retain strong nonlinearity due tostrong FM fluctuations.

The gate tuning of carrier density can be best demonstrated bythe Hall measurements at T¼ 80K (See Supplementary Note 1for details), when the influence of FM fluctuation is muchreduced. Figure 1c shows the Vg-dependent nominal carrierdensity nH estimated from the ordinary Hall coefficient RH asnH¼ 1/RH. The most dramatic feature here is the divergentbehaviour around Vg¼ þ 2V, when the sample is in the chargeneutral regime with EF lying close to the DP16. On the left (right)side, EF lies below (above) the DP with hole-type (electron-type)carriers tuned systematically by Vg. At the large Vg limit close to±15V, the bulk band carriers start to dominate the chargetransport. The same trend is revealed by the longitudinalresistivity rxx measured under varied gate voltages. As shownin Fig. 1e, at Vg¼±15V, the rxx shows a metallic behaviour athigh T and becomes weakly insulating at low T. As EF is tunedtowards the DP, the rxx value keeps rising and the high Tbehaviour gradually becomes insulating between Vg¼ � 2V andþ 4V. These results are consistent with the Hall effectmeasurements and confirm that the bulk is insulating in thisregime but becomes metallic at higher Vg.

MR behaviour of the FM TI film. Figure 2a illustrates theH-dependent MR ratio, defined as

drr0

¼ rxxðHÞ� rxxð0Þrxxð0Þ

ð1Þ

measured at T¼ 1.5 K under varied gate voltages (the raw rxxversus H curves are documented in Supplementary Note 2). Thebutterfly-shaped hysteresis is characteristic of the negative MR inFM metals caused by the spin-dependent scattering of carriers bylocal magnetic ordering2. The peak position corresponds to thecoercive field (HC), and on either side of HC the reducedscattering of a specific spin orientation leads to negative MR.When Vg is reduced to 0 from ±15V, HC decreasesmonotonically. The MR behaviour at T¼ 5K (Fig. 2b) issimilar, except that the HC value is much smaller (note thechange of scale). Figure 2c summarizes the Vg and T dependenceof HC in a colour contour plot. The general trend is a ‘V’-shapedpattern with apparent asymmetry, where the hole-doped side hasstronger FM order. The Curie temperature TC can be estimatedfrom the temperature when HC drops to 0, as shown by the thickblue line. The contour plot clearly demonstrates the enhanced FMorder on both sides of the DP, when more carriers are injectedinto the film by electrical field. The same conclusion can be drawnfrom the contour plot of gate-tuned anomalous Hall effect shownin Supplementary Fig. 3. In fact this ‘V’-shaped gate voltagedependence of HC was already present, although totallyoverlooked, in our previous work on a similar magnetic TI17.As shown clearly in Fig. 2a of ref. 17, HC is smallest aroundVg¼ � 1.5 V, when EF lies in the magnetic gap at the DP andanomalous Hall effect is quantized. HC increases on either side ofthe DP (for example, the Vg¼ � 55 and 200V curves apparentlyhave larger HC than the Vg¼ � 1.5V curve), in good agreementwith the trend observed here.

The MR behaviour at higher temperatures is even moreperplexing. Figure 3a displays the Vg-dependent MR curvesmeasured at T¼ 8K. The Vg¼ � 15V curve still shows thenegative MR similar to that observed at lower temperatures,except that the hysteresis is barely visible due to much reducedHC. With decreasing negative Vg to � 2V, the negative MRremains qualitatively the same although the amplitude keepsdecreasing. At Vg¼ 0V, the MR is still negative at very weak H,but crossovers to positive for H40.1 T. At positive Vg up toþ 4V, the MR exhibits a sharp positive increase with H, but atVg¼ þ 7V the curve returns to the behaviour similar to that at

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Vg¼ 0V with a negative dip at weak H and a slow positiveincrease at higher H. With further increase of positive Vg up toþ 15V, the MR behaviour becomes the same to the regime withlarge negative Vg, showing strongly negative MR. This unusuallycomplex evolution of MR with varied Vg is also seen at highertemperatures. The main change with increasing T is in general thepositive MR becomes more pronounced.

Correlation between MR and ferromagnetism. Figure 4a,bsummarizes the T-dependent MR curves measured at two

representative gate voltages. The position of EF corresponding toeach Vg is shown in the schematic band structure in Fig. 4c,d. It isclear that when EF lies way below the DP (Vg¼ � 15V) and cutsthrough the bulk valence band, the negative MR behaviour dom-inates at all temperatures. In contrast, when EF lies close to the DP(Vg¼ þ 2V) and within the bulk band gap, MR becomes positivefor the whole H range for TZTC¼ 8K, as well as the large Hregime for ToTC. Similar T-dependent MR curves measured atother values of Vg are shown in Supplementary Fig. 4. The overallevolution of MR can be directly visualized in Fig. 4e, where acolour scale is used to characterize the relative MR ratio measured

Vg

TI film

Te Ti/Au

In

–2 –1 0 1–4

–2

0

2

4

–2 –1 0 1 –2 –1 0 1 –2 -1 0 1 –2 –1 0 1 –2 –1 0 1 –2 –1 0 1 –2 –1 0 1 –2 –1 0 1 –2 –1 0 1 2

1.5 K 3 K 5 K 8 K 10 K 12 K 15 K

0 25 50 752

4

6

8

10

12

0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 0 25 50 75 100

–15 –10 –5 0 5 10 15

–10

-5

0

5

10

T = 80 K

n H (

1012

cm

–2)

Vg (V)

Vg= –15 V Vg= –10 V Vg= –5 V Vg= –2 V Vg= 0 V Vg= 2 V Vg= 4 V Vg= 7 V Vg= 10 V Vg= 15 V

Vg= –15 V Vg= –10 V Vg= –5 V Vg= –2 V Vg= 0 V Vg= 2 V Vg= 4 V Vg= 7 V Vg= 10 V Vg= 15 V

� yx(

kΩ)

� xx(

kΩ)

T (K) T (K) T (K) T (K) T (K) T (K) T (K) T (K) T (K) T (K)

�0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T ) �0H (T )

SrTiO3 substrate

Al2O3

Figure 1 | Measurement setup and electrical characterization of the field effect transistor. (a) A FM TI thin film consists of two layers of Dirac

fermions separated by the bulk FM layer. The Dirac fermions residing on the two surfaces have opposite spin chirality. A gap is opened at the DP due

to the out-of-plane ferromagnetism. (b) Schematic device for the magnetotransport measurement of the Cr0.15(Bi0.1Sb0.9)1.85Te3 thin film. A Hall bar

geometry is used to measure the rxx and ryx simultaneously under various gate voltages and magnetic field. (c) Electric field dependence of carrier density

at 80K. Carrier density is estimated from the Hall curve at 80K. The carrier density shows divergent behaviour around Vg¼ þ 2V. (d) Temperature

dependence of the anomalous Hall effect under various gate voltages. Strong FM order is confirmed by the square-shaped hysteresis at 1.5 K over all the

gate voltages. The ordinary Hall slope evolves from positive to the negative when the EF is tuned across the DP. (e) Temperature dependence of 2D

longitudinal resistivity under varied gate voltages. The high Tmetallic behaviour at large |Vg| gradually becomes insulating as EF is tuned into the bulk gap by

the gate voltage.

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at m0H¼ 0.3 T, which is beyond the HC of all curves to avoidcomplications from hysteresis. Interestingly, there is a close cor-relation between the MR ratio shown here and the HC plot in

Fig. 2e, both showing a ‘V’-shaped pattern centred around Vg¼þ 2V. In particular, negative MR is favoured in the regime withstronger ferromagnetism, both in terms of temperature and gate

–15 –10 –5 0 5 10 15

2

4

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0 120

TC

30

27

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0.00

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0.10

�0H (T) �0H (T )

δ�/�

0 (%

)

Vg Vg

–15 V –15 V

–10 V –10 V

–5 V

–2 V0 V2 V

4 V

7 V

10 V

15 V

–5 V

–2 V0 V2 V4 V

7 V

10 V

15 V

10

9

8

7

6

5

4

3

2

1

0

Vg (V)

Hc (mT)

T (

K)

Figure 2 | Magnetotransport results at low temperature and evolution of HC and TC. (a,b) MR measured at T¼ 1.5 K (a) and 5K (b). Each curve is offset

by 3% (a) and 1% (b) for clarity. Butterfly-shaped hysteresis confirms the FM order at low temperature. The negative MR is due to local magnetic order

induced spin-dependent scattering. TC reaches a minimum at þ 2V and increases on both sides, indicating enhanced FM order in both p- and n-type

regime. The increasing temperature reduces the HC and relative change of MR. (c) Summary of the HC and TC at various gate voltages. TC is defined as the

temperature when HC reaches zero within experimental uncertainty. Error bar is due to the discrete temperature points in the measurements. The

asymmetry behaviour of the Vg-dependent TC suggests that the hole-doped regime has stronger FM order.

–4

0

–4

0

–2

0

–2

0

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2

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4

0

2

–1

0

–1

0

–15 VT = 8 K

–10 V

–5 V

–2 V

0 V

2 V

4 V

7 V

10 V

15 V

–4

0

–4

0

–2

0

–2

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–15 VT = 10 K

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– 2 V

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10 V

15 V

–4

0

–4

0

–2

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10 V

15 V

–4

0

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0

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–15 V

–10 V

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0 V

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10 V

15 V

–1.0

–0.5 0.0

0.5

1.0

–1.0

–0.5 0.0

0.5

1.0

–1.0

–0.5 0.0

0.5

1.0

–1.0

–0.5 0.0

0.5

1.0

T = 15 KT = 12 K

��/�

0(%

)

�0H (T ) �0H (T ) �0H (T ) �0H (T )

Figure 3 | Evolution between magnetism-induced negative MR and topology-induced WAL. Gate voltage dependence of MR at various temperatures.

At T¼ 8K (a) magnetism-induced negative MR at � 15V gradually evolves to the topology-induced WAL behaviour as the gate voltage is swept to

þ 2V, but with further increase of Vg up to þ 15V the MR becomes negative again as that in the p-type regime. Similar trend is observed at T¼ 10K

(b) 12 K (c) and 15 K (d).

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voltage. The same pattern can also be seen in the contour plot ofMR taken at other magnetic fields (See Supplementary Note 5 fordetails).

DiscussionIt is very puzzling why the MR has such a complex evolution withgate voltage. In conventional FM metals or diluted magneticsemiconductors, the amplitude of MR may depend on carrierdensity18 but a sign change is rare. Here, we show that in a FM TIfilm, the sign of MR can change twice as the gate voltage is variedbetween ±15V at certain temperature range (Fig. 3a–c). Next,we will unravel the mechanism of this peculiar behaviour, whichrepresents a novel transport phenomenon in TIs withspontaneous FM order.

At first glance, the results shown in Fig. 3 are reminiscent ofthe crossover between WAL and weak localization (WL)proposed for magnetically doped TI19, but a closer examinationof the data suggests otherwise. In pristine TI, spin-momentumlocking of the Dirac cone induces a p Berry phase between twotime-reversed self-crossing loops20. The destructive quantuminterference between them leads to WAL, and magnetic fieldpenetrating the loops suppresses the interference and causes apositive MR11,21,22. WAL indicates that the Dirac fermionscannot be localized by nonmagnetic impurities, which is a keyaspect of the topological protection3,5. Magnetism introducedinto TI breaks the TRS and opens a gap at the DP23,24. The Berryphase f in this case can be expressed as:

f ¼ pð1� D2EF

Þ; ð2Þ

which depends on the gap size D and position of EF (ref. 19).When EF lies close to the DP, f approaches zero, thereby MRshould be negative due to WL. However, Fig. 3 shows that MR ispositive for EF close to DP and becomes negative for EF at higherenergies. This trend is totally opposite to that predicted by the

Berry phase picture and indicates that novel physics beyondsimple localization must be at work.

We gain key insight into this puzzle from the intimaterelationship between MR and ferromagnetism. Let’s first focus onthe limit of Vg¼ � 15V, which has the strongest FM order. Here,EF cuts through the bulk valence band so that bulk holes makedominant contribution to charge transport (Fig. 4c). At lowtemperatures (Tr5K) the MR is negative with pronouncedbutterfly-shaped hysteresis, which is the same as that commonlyobserved in FM metals due to the spin-dependent scattering ofcharge carriers. With increasing temperature to above TC, thelong-range FM order vanishes but strong FM fluctuations makethe physics still valid. As shown in Fig. 4a, from 1.5 to 15K, theMR curves remain qualitatively the same except for the gradualdisappearance of HC. The negative MR of the bulk carriers in FMTI thus has little difference from the magnetism-induced negativeMR in conventional FM metals, which is not totally unexpected.The irrelevance of the WL picture in this regime is furthersupported by the unphysical fitting parameters when we use theHikami–Larkin–Nagaoka formula for localization23 to simulatethe magnetoconductivity curves (see Supplementary Note 6 fordetails).

As EF is moved towards DP by the gate voltage (Vg¼ þ 2V),the charge transport predominantly comes from the surfacestates because EF lies in the bulk gap (Fig. 4d). At TZTC¼ 8 K,there is no long-range FM order; thus, the Dirac cone is gapless.The positive MR in this regime is characteristic of the WAL ofsurface Dirac fermions, just like that in pristine TI. In thisregime, the magnetoconductivity curves can be fitted very wellby the Hikami–Larkin–Nagaoka formula with reasonableparameters showing the WAL behaviour (SupplementaryFig. 6). On cooling to below TC, however, the system showsthe butterfly-shaped negative MR at weak H. Therefore, even thesurface Dirac fermions exhibit rather conventional spin-dependent scattering with local magnetization. As has beenshown by recent angle-resolved photoemission spectroscopy

–15 –10 –5 0 5 10 15

2

4

6

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12

1415

T(K

)

–0.024 –0.012 0.000 0.012

–0.8 –0.4 0.0 0.4 0.8–2

0

2

4

6

8

–0.8 –0.4 0.0 0.4 0.8–4

–2

0

2

4

6

8

Vg = 2 VVg = –15 V

BVB

BCB

BVB

BCB

1.5 K

3 K

5 K

8 K

10 K

12 K

15 K

Γ MK Γ MK

δ�/�

0 (%

)

EF

EF

�0H (T ) �0H (T )

δ�/�0 (�0H = 0.3 T)

Vg (V)

Figure 4 | Correlation between negative MR and ferromagnetism. (a,b) Temperature dependence of MR at two representative gate voltages.

(a) Vg¼ � 15V. As the EF cuts through the bulk valence band, negative MR is observed over all temperature. Each curve is offset by 1.5% for clarity.

(b) Vg¼ 2V. When the EF is tuned into the bulk gap, WAL begin to take charge the transport and WAL is observed above TC. Each curve is offset by

1% for clarity. (c,d) The position of EF at the two gate voltages Vg¼ � 15V (c) and Vg¼ þ 2V (d). (e) Colour plot of the relative change of

MR at m0H¼0.3 T. Negative MR is more pronounced in the regime of high Vg and low temperature, which are favourable for the enhancement of

ferromagnetism.

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measurements, the long-range FM order opens a gap at the DP24

and leads to a hedgehog spin texture for states outside themagnetic gap25. The spins of the Dirac fermions in this regimeobtain an out-of-plane component, and will suffer spin-dependent scattering with the local magnetization. Now themassive Dirac fermions behave more like conventional fermionsdue to the suppression of topological protection by broken TRS.Only at H higher than HC does the MR recover the positivetendency, manifesting the WAL due to residual topologicalprotection.

Therefore, the perplexing MR behaviour actually reflects thecompetition between topology-induced WAL and magnetism-induced negative MR. In the large Vg regime where FM order isstronger and bulk conduction prevails, MR is negative in asimilar manner to conventional FM metal. In the Vg range whenEF lies in the bulk gap and surface Dirac fermions are mainlyresponsible for charge transport, MR is positive due to the WALeffect except for the weak field regime in the FM state. The MRbehaviour at intermediate Vg can be described as the competi-tion of these two effects (Supplementary Fig. 3). The versatileelectrical control of ferromagnetism and MR also allow usto construct novel spintronic and topological magnetoelectricdevices using magnetic TIs. For example, the fact that the signof MR switches twice when Vg is changed between ±15Vmay be used to achieve novel magnetic readout and signaltransmission functions. In certain sense, this is analogousto the famous single electron transistor, which turns on andoff again every time one electron is added to the quantum dot byVg (ref. 26).

The only remaining question is why the FM order isstrengthened by increased carrier density (Fig. 2c). The originof magnetism in TI has attracted much recent attention.Available proposals include the bulk van Vleck mechanism27

and surface Dirac fermion mediated Ruderman–Kittel–Kasuya–Yosida (RKKY) mechanism28. The former one is insensitiveto the carrier density15, whereas in the latter one FM orderbecomes weaker when EF moves away from the DP29. Ourgate tuning results provide a new trend that has neverbeen reported before. The enhanced FM order at heavilyelectron- and hole-doped regime, when the charge transportis dominated by bulk carriers, suggests that the RKKYmechanism involving itinerant bulk carriers is also essential.In fact, it has been shown that in Cr-doped Sb2Te3, the bulkvalence band holes plays an important role in ferromagnetism13,but it has yet to be revealed if the bulk conduction-bandelectrons can do the same thing. Our experimental data shownin Fig. 2c suggest so, although there is an apparent electron-holeasymmetry. This is different from the well-known III–V groupdiluted magnetic semiconductor, in which only hole-type RKKYis available30. A plausible reason is that the TIs have invertedbulk band structure, in which the original bulk conduction/valence bands are hybridized thus share common characteristics.Therefore, bulk electrons can mediate FM order in a similarmanner to the bulk band holes, which is unique to the TIs. Wenote that further theoretical studies with realistic band structureof magnetically doped TI will be needed to confirm thishypothesis.

MethodsSample growth and device fabrication. The Cr0.15(Bi0.1Sb0.9)1.85Te3 TI thin filmwith thickness of five quintuple layers is grown on insulating SrTiO3(111) substrateby using molecular beam epitaxy. The film is covered with 10 nm Te capping layerbefore being taken out of the molecular beam epitaxy chamber. A 50-nm-thickamorphous Al2O3 film deposited by atomic layer deposition is used as the dielectriclayer for the top gate. The sample is fabricated into a Hall bar geometry by usingphotolithography. The length between the longitudinal contacts is 50 mm and widthof the sample is 50 mm. Electric contacts are made by mechanically pressing Indium

into the film. The 2D Hall resistivity ryx and longitudinal resistivity rxx are mea-sured by using standard four-probe ac lock-in method with the magnetic fieldapplied perpendicular to the film plane.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5915

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AcknowledgementsThis work was supported by the National Natural Science Foundation of China, theMinistry of Science and Technology of China and the Chinese Academy of Sciences.

Author contributionsK.H., X.M., Q.X. and Y.W. designed the experiments. X.F., K.L. and Y.O. carried outmolecular beam epitaxy sample growth and device fabrication. Z.Z., M.G., J.Z. and Y.F.carried out transport measurements. L.W., X.C. and X.M. assisted in the experiments.Z.Z., K.H., Q.X. and Y.W. prepared the manuscript. All authors have read and approvedthe final version of the manuscript.

Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Zhang, Z. et al. Electrically tuned magnetic order andmagnetoresistance in a topological insulator. Nat. Commun. 5:4915 doi: 10.1038/ncomms5915 (2014).

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms5915 ARTICLE

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